An Eddy-Resolving Reynolds Stress Transport Model for Unsteady Flow Computations

  • R. Maduta
  • S. Jakirlic
Part of the Notes on Numerical Fluid Mechanics and Multidisciplinary Design book series (NNFM, volume 117)

Abstract

The present work deals with the development of an instability-sensitive turbulence model on the Second-Moment Closure level and its application to flow configurations of increasing complexity featured by boundary layer separation. The model scheme adopted, functioning as a ‘sub-scale’ model in the Unsteady RANS framework, represents a differential near-wall Reynolds stress model formulated in conjunction with the scale-supplying equation governing the homogeneous part of the inverse turbulent time scale ω h (ω h  = ε h / k ). The latter equation was straightforwardly obtained from the model equation describing the dynamics of the homogeneous part ε h (ε h  = ε − 0.5ν ∂ 2 k / ( ∂ x j  ∂ x j ), Jakirlic and Hanjalic, 2002) of the total viscous dissipation rate ε by applying the derivation rules to the expression for ω h . The model capability to account for the vortex length and time scales variability was enabled through a selective enhancement of the production of the dissipation rate in line with the SAS proposal (Scale-Adaptive Simulation, Menter and Egorov, 2010) pertinent particularly to the highly unsteady separated shear layer region. The predictive performances of the proposed model (solved in conjunction with the Jakirlic and Hanjalic’s Reynolds stress model equation) were tested by computing the fully-developed channel flow at different Reynolds numbers, backward-facing step flow, periodic flow over a smoothly contoured 2-D hill in a range of Reynolds numbers and flow in a 3D-diffuser.

Keywords

Direct Numerical Simulation Reynolds Stress Separate Shear Layer Reynolds Stress Model RANS Model 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Breuer, M.: New Reference Data for the Hill Flow Test Case. DFG-CNRS Research Group on “LES of Complex Flows” (2005), http://www.hy.bv.tum.de/DFG-CNRS/
  2. Chaouat, B., Schiestel, R.: A new partially integrated transport model for subgrid-scale stresses and dissipation rate for turbulent developing flows. Phys. Fluids 17(065106), 1–19 (2005)Google Scholar
  3. Cherry, E.M., Elkins, C.J., Eaton, J.K.: Geometric sensitivity of three-dimensional separated flows. Int. J. of Heat and Fluid Flow 29, 803–811 (2008)CrossRefGoogle Scholar
  4. Fröhlich, J., Mellen, C.P., Rodi, W., Temmerman, L., Leschziner, M.A.: Highly resolved large-eddy simulation of separated flow in a channel with streamwise periodic constrictions. J. Fluid Mech. 526, 19–66 (2005)MathSciNetMATHCrossRefGoogle Scholar
  5. Girimaji, S.S.: Partially-Averaged Navier-Stokes Model for Turbulence: A Reynolds-Averaged Navier-Stokes to Direct Numerical Simulation Bridging Method. Journal of Applied Mechanics 73, 413–421 (2006)MATHCrossRefGoogle Scholar
  6. Hoyas, S., Jimenez, J.: Scaling of the velocity fluctuations in turbulent channels up to Reτ = 2003. Physics of Fluids 18(1), 11702 (2006)CrossRefGoogle Scholar
  7. Jakirlić, S., Jester-Zürker, R., Tropea, C.: Report on 9th ERCOFTAC/IAHR/COST Workshop on Refined Turbulence Modelling, Darmstadt University of Technology, October 9-10, 2001. ERCOFTAC Bulletin, vol. 55, pp. 36–43 (2002)Google Scholar
  8. Jakirlić, S., Hanjalić, K.: A new approach to modelling near-wall turbulence energy and stress dissipation. J. Fluid Mech. 439, 139–166 (2002)Google Scholar
  9. Jovic, S., Driver, D.: Reynolds number effect on the skin friction in separated flows behind a backward-facing step. Experiment in Fluids 18, 464–467 (1995)CrossRefGoogle Scholar
  10. Kornev, N., Hassel, E.: Synthesis of homogeneous anisotropic divergence-free turbulent fields with prescribed second-order statistics by vortex dipoles. Physics of Fluids 19(6), 67101 (2007)CrossRefGoogle Scholar
  11. Le, H., Moin, P., Kim, J.: Direct Numerical Simulation of Turbulent Flow over a Backward-Facing Step. J. Fluid Mech. 330, 349–374 (1997)MATHCrossRefGoogle Scholar
  12. Manceau, R.: Report on 10th ERCOFTAC (SIG-15) Workshop on Refined Turbulence Modelling, October 10-11, 2002. ERCOFTAC Bulletin, vol. 57. University of Poitiers (2003)Google Scholar
  13. Menter, F., Egorov, Y.: The Scale-adaptive Simulation method for unsteady turbulent flow predictions. Part 1: theory and model description. Flow, Turbulence and Combustion 85, 113–138 (2010)MATHCrossRefGoogle Scholar
  14. Moser, R.D., Kim, J., Mansour, N.N.: Direct numerical simulation of turbulent channel flow up to Reτ = 590. Physics of Fluids 11(4), 943–945 (1999)MATHCrossRefGoogle Scholar
  15. Ohlsson, J., Schlatter, P., Fischer, P.F., Henningson, D.S.: DNS of separated flow in a three-dimensional diffuser by the spectral-element method. J. Fluid Mech. 650, 307–318 (2010)MATHCrossRefGoogle Scholar
  16. Rapp, C.: Experimentelle Untersuchung der turbulenten Strömung über periodische Hügel. PhD Thesis, Technical University Munich, Germany (2008)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • R. Maduta
    • 1
  • S. Jakirlic
    • 1
  1. 1.Institute of Fluid Mechanics and Aerodynamics / Center of Smart InterfacesTechnische Universität DarmstadtDarmstadtGermany

Personalised recommendations